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Research Article | Open Access

Blow-up solution and analyticity to a generalized Camassa-Holm equation

Ying Wang, Yunxi Guo( )
Department of Mathematics, Zunyi Normal University, 563006, Zunyi, China
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Abstract

A generalized Camassa-Holm equation with higher order nonlinear term was studied. First, we give a new blow-up criterion and a new blow-up phenomenon to the Cauchy problem for the equation under some conditions. Then, we focus on the analytical solutions for the equation. Finally, we prove the analyticity of solution for the equation.

Keywords

blow-up criterionblow-up phenomenonanalytical solutionsanalyticitya generalized Camassa-Holm equation
CLC number: 35D05, 35G25, 35L05, 35Q35

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AIMS Mathematics
Volume 8 Issue 5,
May 2023
Pages 10728-10744
DOI: 10.3934/math.2023544

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Cite this article:
Wang Y, Guo Y. Blow-up solution and analyticity to a generalized Camassa-Holm equation. AIMS Mathematics, 2023, 8(5): 10728-10744. https://doi.org/10.3934/math.2023544

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Received: 15 December 2022
Revised: 14 February 2023
Accepted: 22 February 2023
Published: 15 May 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)